Exercise 58 Page 690

For any △ ABC, let the lengths of the sides opposite angles A, B, and C be a, b, and c, respectively.

sin A/a=sin B/b=sin C/c Let's use this law to find the value of x. Consider the given triangle.

We know that the length of a side is 23 and that the measure of its opposite angle is 21^(∘). We want to find the length of the side that is opposite to the angle whose measure is 128^(∘). With this information and using the Law of Sines, we can write an equation in terms of x. sin 21^(∘)/23=sin 128^(∘)/x Let's solve the above equation for x using the Cross Product Property.

sin 21^(∘)/23=sin 128^(∘)/x

CrossMult

Cross multiply

sin 21^(∘)* x=23* sin 128^(∘)

DivEqn

.LHS /sin 21^(∘).=.RHS /sin 21^(∘).

x=23* sin 128^(∘)/sin 21^(∘)

UseCalc

Use a calculator

x=50.57440...

RoundDec

Round to 1 decimal place(s)

x≈ 50.6